21 research outputs found
Integrable deformations of strings on symmetric spaces
A general class of deformations of integrable sigma-models with symmetric
space F/G target-spaces are found. These deformations involve defining the
non-abelian T dual of the sigma-model and then replacing the coupling of the
Lagrange multiplier imposing flatness with a gauged F/F WZW model. The original
sigma-model is obtained in the limit of large level. The resulting deformed
theories are shown to preserve both integrability and the equations-of-motion,
but involve a deformation of the symplectic structure. It is shown that this
deformed symplectic structure involves a linear combination of the original
Poisson bracket and a generalization of the Faddeev-Reshetikhin Poisson bracket
which we show can be re-expressed as two decoupled F current algebras. It is
then shown that the deformation can be incorporated into the classical model of
strings on R x F/G via a generalization of the Pohlmeyer reduction. In this
case, in the limit of large sigma-model coupling it is shown that the theory
becomes the relativistic symmetric space sine-Gordon theory. These results
point to the existence of a deformation of this kind for the full Green-Schwarz
superstring on AdS5 x S5.Comment: 41 pages, typos corrected, references adde
S-matrices and quantum group symmetry of k-deformed sigma models
Recently, several kinds of integrable deformations of the string world sheet theory in the gauge/gravity correspondence have been constructed. One class of these, the k deformations associated to the more general q deformations but with q=exp(i pi/k) a root of unity, has been shown to be related to a particular discrete deformation of the principal chiral models and (semi-)symmetric space sigma models involving a gauged WZW model. We conjecture a form for the exact S-matrices of the bosonic integrable field theories of this type. The S-matrices imply that the theories have a hidden infinite dimensional affine quantum group symmetry. We provide some evidence, via quantum inverse scattering techniques, that the theories do indeed possess the finite-dimensional part of this quantum grou
An integrable deformation of the AdS5×S5superstring
The S-matrix on the world-sheet theory of the string in AdS5 x S5 has
previously been shown to admit a deformation where the symmetry algebra is
replaced by the associated quantum group. The case where q is real has been
identified as a particular deformation of the Green-Schwarz sigma model. An
interpretation of the case with q a root of unity has, until now, been lacking.
We show that the Green-Schwarz sigma model admits a discrete deformation which
can be viewed as a rather simple deformation of the F/F_V gauged WZW model,
where F=PSU(2,2|4). The deformation parameter q is then a k-th root of unity
where k is the level. The deformed theory has the same equations-of-motion as
the Green-Schwarz sigma model but has a different symplectic structure. We show
that the resulting theory is integrable and has just the right amount of
kappa-symmetries that appear as a remnant of the fermionic part of the original
gauge symmetry. This points to the existence of a fully consistent deformed
string background.Comment: 23 pages, improved and expanded discussion of metric and B fiel
The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
The generalized symmetric space sine-Gordon theories are a series of
1+1-integrable field theories that are classically equivalent to superstrings
on symmetric space spacetimes F/G. They are formulated in terms of a
semi-symmetric space as a gauged WZW model with fermions and a potential term
to deform it away from the conformal fixed point. We consider in particular the
case of PSU(2,2|4)/Sp(2,2)xSp(4) which corresponds to AdS(5)xS(5). We argue
that the infinite tower of conserved charges of these theories includes an
exotic N=(8,8) supersymmetry that is realized in a mildy non-local way at the
Lagrangian level. The supersymmetry is associated to a double central extension
of the superalgebra psu(2|2)+psu(2|2) and includes a non-trivial R symmetry
algebra corresponding to global gauge transformations, as well as 2-dimensional
spacetime translations. We then explicitly construct soliton solutions and show
that they carry an internal moduli superspace CP(2|1)xCP(2|1) with both bosonic
and Grassmann collective coordinates. We show how to semi-classical quantize
the solitons by writing an effective quantum mechanical system on the moduli
space which takes the form of a co-adjoint orbit of SU(2|2)xSU(2|2). The
spectrum consists of a tower of massive states in the short, or atypical,
symmetric representations, just as the giant magnon states of the string world
sheet theory, although here the tower is truncated.Comment: 39 pages, references adde
Alleviating the non-ultralocality of coset sigma models through a generalized Faddeev-Reshetikhin procedure
The Faddeev-Reshetikhin procedure corresponds to a removal of the
non-ultralocality of the classical SU(2) principal chiral model. It is realized
by defining another field theory, which has the same Lax pair and equations of
motion but a different Poisson structure and Hamiltonian. Following earlier
work of M. Semenov-Tian-Shansky and A. Sevostyanov, we show how it is possible
to alleviate in a similar way the non-ultralocality of symmetric space sigma
models. The equivalence of the equations of motion holds only at the level of
the Pohlmeyer reduction of these models, which corresponds to symmetric space
sine-Gordon models. This work therefore shows indirectly that symmetric space
sine-Gordon models, defined by a gauged Wess-Zumino-Witten action with an
integrable potential, have a mild non-ultralocality. The first step needed to
construct an integrable discretization of these models is performed by
determining the discrete analogue of the Poisson algebra of their Lax matrices.Comment: 31 pages; v2: minor change
Giant magnons of string theory in the lambda background
The analogues of giant magnon configurations are studied on the string world
sheet in the lambda background. This is a discrete deformation of the
AdS(5)xS(5) background that preserves the integrability of the world sheet
theory. Giant magnon solutions are generated using the dressing method and
their dispersion relation is found. This reduces to the usual dyonic giant
magnon dispersion relation in the appropriate limit and becomes relativistic in
another limit where the lambda model becomes the generalized sine-Gordon theory
of the Pohlmeyer reduction. The scattering of giant magnons is then shown in
the semi-classical limit to be described by the quantum S-matrix that is a
quantum group deformation of the conventional giant magnon S-matrix. It is
further shown that in the small g limit, a sector of the S-matrix is related to
the XXZ spin chain whose spectrum matches the spectrum of magnon bound states.Comment: 53 pages, 6 figures, final version to appear in JHE
The structure of non-abelian kinks
We consider a class of integrable quantum field theories in 1+1 dimensions
whose classical equations have kink solutions with internal collective
coordinates that transform under a non-abelian symmetry group. These
generalised sine-Gordon theories have been shown to be related to the world
sheet theory of the string in the AdS/CFT correspondence. We provide a careful
analysis of the boundary conditions at spatial infinity complicated by the fact
that they are defined by actions with a WZ term. We go on to describe the local
and non-local charges carried by the kinks and end by showing that their
structure is perfectly consistent with the exact factorizable S-matrices that
have been proposed to describe these theories.Comment: 41 pages, more typos correcte
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Huygens-Fresnel Wave-Optics Simulation of Atmospheric Optical Turbulence and Reflective Speckle in CO
The measurement sensitivity of CO{sub 2} differential absorption LIDAR (DIAL) can be affected by a number of different processes. Two of these processes are atmospheric optical turbulence and reflective speckle. Atmospheric optical turbulence affects the beam distribution of energy and phase on target. The effects of this phenomenon include beam spreading, beam wander and scintillation which can result in increased shot-to-shot signal noise. In addition, reflective speckle alone has been shown to have a major impact on the sensitivity of CO{sub 2} DIAL. The authors have previously developed a Huygens-Fresnel wave optics propagation code to separately simulate the effects of these two processes. However, in real DIAL systems it is a combination of these phenomena, the interaction of atmospheric optical turbulence and reflective speckle, that influences the results. In this work, the authors briefly review a description of the model including the limitations along with a brief summary of previous simulations of individual effects. The performance of the modified code with respect to experimental measurements affected by atmospheric optical turbulence and reflective speckle is examined. The results of computer simulations are directly compared with lidar measurements and show good agreement. In addition, simulation studies have been performed to demonstrate the utility and limitations of the model. Examples presented include assessing the effects for different array sizes on model limitations and effects of varying propagation step sizes on intensity enhancements and intensity probability distributions in the receiver plane